MSE 3143 Ceramic Materials
Crystal Structures of Ceramics
Assoc.Prof. Dr. Emre YALAMAÇ Res.Asst. B.Şölen AKDEMİR
2017-2018 Fall 1
OUTLINE
ATOMS, ELECTRONIC STRUCTURE OF ATOMS, INTERATOMIC BONDS
THE CRYSTAL STRUCTURES AND PROPERTIES OF CERAMICS
2 ATOMS, ELECTRONIC STRUCTURE OF ATOMS, INTERATOMIC BONDS
The Atom Energy Levels, Orbital and Quantum Numbers Electron distribution and Orbital Diagram Ionic Diameter Interatomic Bonds Electronegativity and Polar Bonds
3
THE ATOM
4 ENERGY LEVELS, ORBITAL AND QUANTUM NUMBERS
Energy levels (shell): A shell specifies the energy levels of the atom and defines as n Lower energy levels (subshell): Atomic energy levels are composed of lower energy levels or subshells. It is defined as orbitals and every subshells has specific notations, n and l
l : 0 s l : 1 p l : 2 d l : 3 f
Orbital: An orbital is specified by n, l, and ml, and can contain a maximum of two electrons with opposite spins Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007 5
ENERGY LEVELS, ORBITAL AND QUANTUM NUMBERS Quantum Numbers
Four quantum numbers are necessary to specify the state of any electron: 1. n principal quantum number 2. l orbital shape, or orbital angular momentum, quantum number
3. ml orbital orientation, or orbital magnetic, quantum number
4. ms spin, or spin magnetic, quantum number
Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007 6 ENERGY LEVELS, ORBITAL AND QUANTUM NUMBERS Quantum Numbers Are these numbers important for ceramics ? The answer, of course, is YES. The color of a ceramic, such as ruby, derives directly from transitions between energy levels. The energy levels are the result of which orbitals are occupied and their relative energies.
We use transitions for chemical analysis of ceramics—certain transitions are allowed (quantum mechanical selection rules).
Magnetism relates directly to the spin of the electrons. If we have more spins up than down then we have magnetization.
Atomic arrangements in covalently bonded ceramics can be understood by considering hybridization of atomic orbitals. It is the sp3 hybridization of atomic orbitals in carbon that allows the tetrahedral arrangement of atoms in diamond. The s and the p in sp3 refer to the atomic orbitals. 7
ELECTRON DISTRIBUTION AND ORBITAL DIAGRAM
• Electrons are settled at orbitals according to lowering the energy of atom • These electrons are located in compliance with Pauli exclusion principle:
No two electrons in an atom can have the same set of four quantum numbers
# Electron distribution is shown as: nl Example: 1s1 and 1s2
8 ELECTRON DISTRIBUTION AND ORBITAL DIAGRAM Orbital Diagram
electron spin and the lower shell group
IONIC DIAMETER
• Cations are smaller than the atoms which they form
• For isoelectronic cations; the higher the ionic charge the smaller the ionic radius
• Anions are bigger than the atoms which they are formed. For isoelectronic anions; the higher the ionic charge the greater the ionic radius
10 INTERATOMIC BONDS
• Interatomic bonds form the internal structure by holding atoms together. • Most properties of materials are highly depend on their internal structures.
• Elastic modulus Strong • Thermal expansion • Strength bond • Melting point
• Interatomic bonds are originated from electrostatic attraction or coulomb forces between oppositely charged particles.
Net For neutral # of # of electrical atoms electrons protons charge 0
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INTERATOMIC BONDS
• Elements with unfilled electron shells are not as stable interact with other atoms in a controlled fashion such that electrons are shared or exchanged between these atoms to achieve stable full outer shells.
• In discussing ceramics, we usually think of the material in terms of ions; ions with the same sign always repel one another due to the Coulomb force.
• Atoms have specific potential energies individually. This potential energy decreases during bond formation, reaches minimum at equilibrium condition. Therefore stable structure forms.
12 INTERATOMIC BONDS We can divide interatomic bonds into two categories:
Primary Secondary (strong) bonds (weak) bonds
Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007 13
INTERATOMIC BONDS Three Chemical Bond Model
14 INTERATOMIC BONDS Ionic Bonding Energy: The importance of lattice energy
• Some exothermic reactions surpass some endothermic steps with released energy from formation of
Li(s) + F2(g) → LiF(s) • This reaction of energy is the strong attraction of oppositely charged ions each other.
+ - ° Li (g) + F (g) → LiF(g) ∆퐻 = −755 푘퐽
• Naturally LiF gas molecules could not exist. Because there has to be excessive amount of released energy to form crystal structure by combination of gas ions. + - ∆퐻°= −1050 푘퐽 Li (g) + F (g) → LiF(s)
• This energy is called as lattice energy of LiF. ° Lattice energy (∆퐻 ) is the enthalpy change formed during decomposition of 1 mol of ionic solid to its gas
ions. It effects some properties like ionic interaction strength, boiling point, hardness and solubility etc. 15
INTERATOMIC BONDS Bond Exchange Between Periodic Elements
• All binary ionic compounds contain metal and non-metal. However not all metals could form binary ionic compounds with all non-metals.
The bond model between berilium (Be) and Ex.: chloride (Cl) is more similar to covalent bonding rather than ionic bonding.
16 INTERATOMIC BONDS Bond Exchange Between Periodic Elements Ionic and Covalent Bonding Compounds
• In most ceramic materials ionic and covalent bonding exist together. CaSO • Composed of both ionic and covalent bonds. 4 Atomic (gypsum) Number of 16 (Having 6 electrons at its outer shell) Sulfide Bonds ionically by giving 2 electrons to the structure
While S O Ca
Bonds covalently 17
ELECTRONEGATIVITY AND POLAR BONDS
• Until now ionic and covalent bonding formed by shared or exchanged electrons is mentioned.
• In reality, bonding type of materials exist between these two.
• Substantial amount of compounds have polar covalent bonding which means partially ionic and partially covalent.
18 ELECTRONEGATIVITY AND POLAR BONDS Electronegativity Electronegativity is a measure of the strength with which an atom in a molecule attracts electrons.
It is the contribution of electrostatic charge.
As shown in the above calculation, F atom attracts shared electrons more than H atom. It means that floride is more electronegative than hydrogen. Therefore while the end of the F atom charges negatively, the end of the H atom charges positively. These partial charges cause increase in the bonding energy.
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ELECTRONEGATIVITY AND POLAR BONDS Electronegativity
Carter, C.B.; Norton, M.G.; ’’Ceramic Materials: Science and Engineering’’, Springer, 2007 20 Crystal Structure Ceramic Structures and Stable Ionic Radius THE CRYSTAL STRUCTURES Cordination Numbers ve Types AND Pauling Rules PROPERTIES OF CERAMICS Polymorphism AX - Type Crystal Structures
AmXp - Type Crystal Structures
AmBnXp - Type Crystal Structures Silicate Structures Carbon Structures
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CRYSTAL STRUCTURES
• Atoms bond together in metals and ceramics in distinct geometric arrangements that repeat throughout the material to form a crystal structure. The crystal structure that results depends upon the type of atomic bonding, the size of the atoms (or ions), and the electrical charge of the ions. • The smallest grouping of atoms that shows the geometry of the structure (and can be stacked as repeating units to form a crystal of the structure) is referred to as the unit cell. • Unit cell is defined as 3 different vectors having origin at the corner of a rectangular coordinate system with axial lengths and interaxial angles.
22 CRYSTAL STRUCTURES – Bravais Lattices
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CERAMIC STRUCTURES AND STABLE IONIC RADIUS
• Ceramics are composed of at least two elements (metallic and non-metallic).
• Because of having more components, it has more complex crystal structures than metals.
• Atomic bonding ranges from purely ionic to totally covalent (most of them exhibit combinations of two)
• In ionic bonding, metal ions (cations) are charged positively. Because they give their valance electrons to negatively charged non-metallic ions (anions).
24 CERAMIC STRUCTURES AND STABLE IONIC RADIUS
• Ionic radius of anions and cations (rA and rC, respectively) are critical parameters effects the crystal structure. • The metallic ions, or cations, are positively charged, because they have given up their valence electrons to the nonmetallic ions, or anions, which are negatively charged. • Because the metallic elements give up electrons when ionized, cations are ordinarily smaller than
anions, and, consequently, the ratio rC/rA is less than unity. • Stable ceramic crystal structures form when those anions surrounding a cation are all in contact with that cation as shown in the figure W.D.,Callister; D.G.,Rethwisch; Material Science and Engineering, 8th Edition, John Wiley&Sons, Inc., 2011
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CORDINATION NUMBERS VE TYPES
• The coordination number (i.e., number of anion nearest neighbors for a cation) is related to the cation–anion radius ratio. • For a specific coordination number, there is a critical or minimum rC/rA ratio. This ratio may be determined from pure geometrical
considerations (Tetrahedral) • The relationships between coordination number and cation–anion radii ratios are based on geometrical considerations and assuming “hard sphere” ions • The most common coordination numbers for ceramics are 4, 6 and 8 (Oktahedral)
W.D.,Callister; D.G.,Rethwisch; Material Science and Engineering, 8th Edition, John Wiley&Sons, Inc., 2011 26 PAULING RULES
• Rule 1: A coordinated polyhedron of anions is formed about each cation. The cation–anion distance is determined by the sum of the two radii and the coordination number is determined by the radius ratio.
• Rule 2: In a stable structure, the total strength of the bonds that reach an L. Pauling (1901-1994) anion in a coordination polyhedron from all neighboring cations should be equal to the charge of the anion. • Rule 3: The polyhedra in a structure tend not to share edges or faces. If the edges are shared, the shared edges are shortened. Shared faces are the least favorable. • Rule 4: Crystals containing different cations of high valence and small coordination number tend not to share polyhedron elements with each other. • Rule 5: The number of essentially different kinds of constituents in a crystal tends to be small.
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CORDINATION NUMBERS VE TYPES
Atomic radius of Fe is 0.124 nm W.D.,Callister; D.G.,Rethwisch; Material Science and Engineering, 8th Edition, John Wiley&Sons, Inc., 2011
28 Example
Predict the coordination number for the ionic solids CsCl and NaCl. Use the following ionic radii for the prediction: (Cs+= 0.170 nm, Na+= 0.102 nm, Cl-= 0.181 nm)
Example
Calculate the ionic packing for CsCl for given ionic radius; (Cs+= 0.170 nm, Cl-= 0.181 nm) POLYMORPHISM
• Materials having the same chemical composition but a different crystal structure are called polymorphs • The change from one structure to another is referred to as a polymorphic transformation • Polymorphism is common in ceramic materials and in many cases has a strong impact on useful limits of application ZnS ZnS ZrO2 Phase Transition (Cubic) (Rhombohedral) at RT at 1100ᵒC
At RT At 1205ᵒC At 2377ᵒC 31
POLYMORPHISM
• Involves distortion of the structure, such as a change in bond angles Displacive • Does not include breaking of bonds Transformation • Is reversible 1 • Martensite, BaTiO3, ZrO2, SiO2
• Bonds are broken and new structure formed Reconstructive • Much greater energy is required for this type of transformation than 2 Transformation for a displacive transformation • SiO2
32 POLYMORPHISM - SiO2
33
POLYMORPHISM
SiO2
• Both displacive and reconstructive tranformations occur in SiO2 and play an important role in silicate technology
• The stable polymorph of SiO2 at room temperature is quartz. However, tridymite and cristobalite are also commonly found at room temperature in ceramic components as
metastable forms because the reconstructive transformations in SiO2 are very sluggish and do not normally occur. • All these three forms have displacive transformations in which the high-temperature structures are distorted by changes in bond angle. • These displacive transformations are rapid and cannot be restrained from occuring.
34 AX - TYPE CRYSTAL STRUCTURES
• Some of the common ceramic materials are those in which there are equal numbers of cations and anions
• These are often referred to as AX compounds, where A denotes the cation and X the anion
• There are several different crystal structures for AX compounds; each is normally named after a common material that assumes the particular structure
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AX - TYPE CRYSTAL STRUCTURES
Cesium Chloride Structure Rock Salt Structure • The coordination number is 8 Zinc Blende Structure, • The coordination number for for both ion types both cations and anions is 6 • The anions are located at (Wurtzite) • the rock salt crystal structure each of the corners of a • the coordination number is may be thought of as two cube, whereas the cube 4; that is, all ions are interpenetrating FCC lattices, center is a single cation tetrahedrally coordinated one composed of the cations, • This is not a BCC crystal • An equivalent structure the other of anions structure because ions of two results if Zn and S atom • NaCl, MgO, MnS, LiF, and FeO different kinds are involved positions are reversed • ZnS, ZnTe, and SiC • CsCl, CsBr ve CsI 36 AmXp- TYPE CRYSTAL STRUCTURES
• If the charges on the cations and anions are not the same, a compound can exist with the chemical
formula AmXp, a coordination number is 8.
• An example would be AX2, for which a common crystal structure is found in fluorite (CaF2)
• Other compounds that have this crystal structure include ZrO2 (cubic structure), UO2, PuO2, and ThO2
Alumina (Al2O3) (Corundum) • The O2- anions are arranged in nearly hexagonal close packing (HCP) • The cations fill 2/3 of the octahedral interstitial sites
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AmBnXp - TYPE CRYSTAL STRUCTURES • It is also possible for ceramic compounds to have more than one type of cation; for two types of
cations (represented by A and B), their chemical formula may be designated as AmBnXp
Perovskite Crystal Structure Calcite Structure
(ABX3) (ABX3) Each C4+ is surrounded by O2- Barium titanate (BaTiO3), having both Ba2+ and Ti4+ anions. Each of these CO3 2+ cations, falls into this groups has six Ca neighbors. classification. It has important This results in a rhombohedral electromechanical properties. unit cell resulting in highly anisotropic propeties
W.D.,Callister; D.G.,Rethwisch; Material Science and Engineering, 8th Edition, John Wiley&Sons, Inc., 2011 Richerson, D.W.; Modern Ceramic Engineering: Properties, Processing and Use in Design, 3rd edition, Taylor&Francis, 2006 38 AmBnXp - TYPE CRYSTAL STRUCTURES
Spinel Structure (AB2X4)
• The spinel structures are cubic with a unit cell containing 32 oxygen ions, 16 octahedral cations, and 8 tetrahedral cations.
The Inverse The Normal Spinel 1 Spinel 2 The A2+ cations The A2+ occupy and half the B3+ 1/8 of the cations occupy tetrahedral sites octahedral sites and the B3+ 1/2 while remaining of the octahedral B3+ cations are sites. on tetrahedral sides 39
AmBnXp - TYPE CRYSTAL STRUCTURES
Spinel Structure (AB2X4)
40 SILICATE STRUCTURES
• Silicates are materials composed primarily of silicon and oxygen, the two most abundant elements in the earth’s crust; consequently, the bulk of soils, rocks, clays, feldpar, mica and sand come under the silicate classification. • They are useful engineering materials because of their low cost, availability and superior properties. • Silicate structures are important for materials used in engineering applications like glass, cement and brick production. Great numbers of electrical insulating materials are made of silicates. ퟒ • The basic unit of the silicates is 푺풊푶ퟒ tetrahedron.
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SILICATE STRUCTURES
Silica (SiO2)
• Chemically, the most simple silicate material is silicon dioxide, or silica (SiO2). • Structurally, it is a three-dimensional network that is generated when the corner oxygen atoms in each tetrahedron are shared by adjacent tetrahedra. • Thus, the material is electrically neutral and all atoms have stable electronic structures. • There are three primary polymorphic crystalline forms of silica: quartz, cristobalite, and tridymite. • Their structures are relatively complicated, and comparatively open; that is, the atoms are not closely packed together. • As a consequence, these crystalline silicas have relatively low densities; 휌 = 2.65 푔⁄푐푚 at RT 42 SILICATE STRUCTURES
Silica Glasses (SiO2)
• Silica can also be made to exist as a noncrystalline solid or glass having a high degree of atomic randomness, which is characteristic of the liquid; such a material is called fused silica, or vitreous silica. • The common inorganic glasses that are used for containers, windows, and so on are silica glasses to which have been added other oxides such as CaO and
Na2O (which are network modifiers).
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SILICATE STRUCTURES
Silicates (SiO2)
• For the various silicate minerals, one, two, or three of the corner oxygen atoms of the ퟒ 푺풊푶ퟒ tetrahedra are shared by other tetrahedra to form some rather complex structures. • Positively charged cations such as Ca2+, Mg2+, and Al3+ compensate the negative charges so that charge neutrality is achieved.
44 CARBON STRUCTURES
• This group of materials does not really fall within any one of the traditional metal, ceramic, or polymer classification schemes. However, because of similarity of crystal structures of graphite, diamond or other polymorphic forms of carbon to that of zinc blende, they are classified as ceramic
Diamond Graphite 45
CARBON STRUCTURES
Fullorene (buckyball) Carbon Nanotube (CNT) Another polymorphic form of carbon was discovered Its structure consists of a single sheet of graphite, in 1985. It exists in discrete molecular form and rolled into a tube, both ends of which are capped consists of a hollow spherical cluster of sixty carbon with C60 fullerene hemispheres. atoms; a single molecule is denoted by C60.
46 Example
If the edge length of the unit cell of MgAl2O4 cubic structure is 809 pm, calculate the theoretical density of magnesium aluminate spinel.
(Al: 26.98 g/mol, Mg: 24.3 g/mol, O: 16 g/mol)